Teaching Mathematics Using History and Fairy Tales Daryl

Teaching Mathematics Using History and Fairy Tales Daryl Stephens and Robert Davidson Department of Mathematical Sciences East Tennessee State University Tennessee Association for Developmental Education 20 th Annual Conference October 28, 2003 – Memphis, Tennessee

Why integrate history and stories into math class? n n n To humanize mathematics Connect real-life experiences with mathematics Show people in the real world use math Relax students and alleviate math anxiety Solve problems Illustrate concepts by stories

Mathematicians Interesting Tidbits

René Descartes (March 31, 1596 – February 11, 1650) Queen Christina Elizabeth of Bohemia

Blaise Pascal (June 19, 1623 – August 19, 1662) Pierre de Fermat (August 17, 1601 – January 12, 1665)

Gerolamo Cardano (September 24, 1501 - September 21, 1576) Niccolo Fontana Tartaglia (1499 or 1500 - December 13, 1557)

Robert Recorde n n Ca. 1510 -1558 Introduced = sign

Christoff Rudolff (1499? -1545? ) n n n Introduced the radical sign, 1525, in a book called Die Coss. √ Stretched-out r Used a vertical bar as a decimal point Used a period for equals Recognized the law b n · b m = b n + m Credited with introducing + and –

Michael Stifel (1486 -1567) n n n “Greatest German algebraist of the 16 th century” Used + and – signs Also credited with modern radical sign Concluded world would end on 10/3/1533. Said Pope Leo X was the Beast in Rev. Magic Squares

Thomas Hariot (1560 -1621) n n n Introduced < and > as we use them today First to write exponents as we do (a 3 instead of aaa) Helped Sir Walter Raleigh map NC Discovered sunspots Died of cancer from tobacco

William Oughtred (1574 -1660) n n Introduced the × for multiplication Introduced : : for proportion and ~ for difference between Clergyman who gave free math lessons Famous pupils: John Wallis, Christopher Wren, Seth Ward

Gottfried Wilhelm von Leibniz (1646 -1716) n n Used both • and for multiplication Calculating machine (first mechanical to multiply and divide) Developed binary numeral system Co-creator of calculus

Johann Heinrich Rann (1622 -1676) n Introduced the ÷ symbol for division (although this symbol was used by many continental Europeans for subtraction).

Christian Kramp (1760 -1826) n n First to use the n! symbol for factorials in 1808 Used because of printing problems with a previously-used symbol

Evariste Galois (1811 - 1832) n n “Unfortunately what is little recognized is that the most worthwhile scientific books are those in which the author clearly indicates what he does not know; for an author most hurts his readers by concealing difficulties. ” Died in a duel over a woman’s love

Connecting Real-life Experiences

Real World Examples n n n Reading blueprints Packing furniture “Inequalities will never affect me!” Emily’s inequalities Calculator project Cartesian inequalities and the tennis court

Relax students and help alleviate math anxiety

Math wasn’t created to make students miserable, but to solve problems! n Religion Pyramids n Astronomy n n Politics n n Sputnik Money n Geometry and Egyptian taxation

Illustrate a point with a story

The Key Story n n n Try turning it upside down! Factor: 21 x 2 – x – 10 (3 x + 5)(7 x – 2) doesn’t work Try switching around to (3 x + 2)(7 x – 5)

Dr. Seuss’s The Sneetches n n n Functions Composite functions Inverse functions

The Cat in the Box Dana Michel, Wonder Books, 1963 n Subsets n Sets of numbers

Trolls and Negative Exponents n Working with rational expressions with negative exponents such as:

“The Elephant and the Squirrel” n n Children’s story by Bill Sprague from A Treasury of Bedtime Stories (ed. Judith Klugmann, Doubleday, 1960). Stop and look at other ways of solving problems besides the obvious!

Your Turn Any stories you’d like to share?

More information This presentation and a handout will be posted on Daryl’s web page late next week. http: //faculty. etsu. edu/stephen/ Look for link on the page. E-mail: stephen@etsu. edu davidson@etsu. edu

Credits n n Except for pictures of books, all images of people came from Wikipedia (www. wikipedia. com) or The Mac. Tutor History of Mathematics archive (http: //www-gap. dcs. stand. ac. uk/~history/index. html) and are in public domain Brown troll and key pictures by Daryl